The thing nobody tells you about neutral storage is that it only looks good when the lid actually fits. A basket with a lid that sits crooked or won't close all the way looks worse than no basket at all, just sitting there gaping open with whatever you shoved inside half spilling out. Check that before anything else.
If you own none of this yet, start with one good sized lidded box for whatever room generates the most loose stuff, usually the living room or a kid's room. Not a set of six, not yet. One box you actually use teaches you more about what you need than a stack you were sold as a bundle. I bought a set of five nesting baskets years ago thinking I'd found the answer to everything, and three of them have never held anything because they're the wrong shape for what I actually own.
On color, the safest choices are the ones that read as texture rather than as decor: raw jute, bleached cotton rope, a plain oatmeal canvas, a pale wood tone. Stay away from anything bright white if you've got a household with any amount of daily use in it, because it shows every mark within a month and starts looking tired fast. A warm, slightly imperfect neutral hides more and ages better. Woven natural fiber in particular earns its keep here, it looks the same at year three as it did on day one, which is more than I can say for the painted canvas boxes I tried first.
Getting the scale right matters more than people expect. Measure the actual space, shelf width, the gap under a console table, the corner of a closet, before you buy anything, and leave an inch or two of breathing room on each side so it doesn't look jammed in. The common mistake is buying too small because a box looks bigger in a photo than it is in your hallway, and the second most common mistake is buying something so large it dwarfs the shelf and becomes the only thing anyone notices in the room. Stack height matters too, if you're going two boxes high, check the lower one can actually hold weight without the sides bowing in.
A cheap box looks fine for about six weeks and then the fibers start fraying at the corners, the lid warps, and it never quite shuts the same way again. A well made one holds its shape through years of being pulled on and off a shelf by someone looking for a charger cable.
This is for anyone whose house collects things faster than it can contain them, and wants the containers to disappear into the room rather than add to the pile.